%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV617-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:19:06 PM UTC 2026
% Result : Unsatisfiable 3.65s 1.22s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 29 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 16 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f773,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f774,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(reorient_equations,[],[f773]) ).
fof(f786,axiom,
! [X0] : c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X0),X0,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
fof(f787,plain,
! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X0),X0,tc_Complex_Ocomplex),
inference(reorient_equations,[],[f786]) ).
fof(f792,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X1,X0) = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f793,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(reorient_equations,[],[f792]) ).
fof(f817,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f818,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
inference(reorient_equations,[],[f817]) ).
fof(f825,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f826,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(reorient_equations,[],[f825]) ).
fof(f905,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f907,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f910,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f919,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(superposition,[],[f826,f787]) ).
fof(f1010,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
inference(superposition,[],[f919,f774]) ).
fof(f1011,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[],[f1010,f907]) ).
fof(f1015,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[],[f1011,f793]) ).
fof(f1016,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[],[f1015,f905]) ).
fof(f1363,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(resolution,[],[f818,f910]) ).
fof(f1507,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(superposition,[],[f1016,f1363]) ).
fof(f1508,plain,
$false,
inference(trivial_inequality_removal,[],[f1507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV617-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 12:03:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.65/1.22 % (1737096)Input is clausal, will run a generic CNF schedule.
% 3.65/1.22 % (1737102)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=475701589:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.65/1.22 % (1737106)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1271010532:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.65/1.22 % (1737101)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2248484935:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.65/1.22 % (1737104)lrs+10_1_sil=8000:sp=occurrence:random_seed=3442112271:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.65/1.22 % (1737103)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2865569393:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.65/1.22 % (1737105)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4210417064:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.65/1.22 % (1737107)dis-21_1_sil=8000:lcm=predicate:random_seed=112932182:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.65/1.22 % (1737106)First to succeed.
% 3.65/1.22 % (1737106)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1737096"
% 3.65/1.22 % (1737104)Instruction limit reached!
% 3.65/1.22 % (1737104)------------------------------
% 3.65/1.22 % (1737104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.22 % (1737104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.22 % (1737104)CaDiCaL version: 2.1.3
% 3.65/1.22 % (1737104)Termination reason: Instruction limit
% 3.65/1.22 % (1737104)Termination phase: Saturation
% 3.65/1.22 % (1737104)Time elapsed: 0.063 s
% 3.65/1.22 % (1737104)Peak memory usage: 89 MB
% 3.65/1.22 % (1737104)Instructions burned: 108 (million)
% 3.65/1.22 % (1737105)Instruction limit reached!
% 3.65/1.22 % (1737105)------------------------------
% 3.65/1.22 % (1737105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.22 % (1737105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.22 % (1737105)CaDiCaL version: 2.1.3
% 3.65/1.22 % (1737105)Termination reason: Instruction limit
% 3.65/1.22 % (1737105)Termination phase: Saturation
% 3.65/1.22 % (1737105)Time elapsed: 0.069 s
% 3.65/1.22 % (1737105)Peak memory usage: 89 MB
% 3.65/1.22 % (1737105)Instructions burned: 114 (million)
% 3.65/1.22 % (1737107)Instruction limit reached!
% 3.65/1.22 % (1737107)------------------------------
% 3.65/1.22 % (1737107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.22 % (1737107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.22 % (1737107)CaDiCaL version: 2.1.3
% 3.65/1.22 % (1737107)Termination reason: Instruction limit
% 3.65/1.22 % (1737107)Termination phase: Saturation
% 3.65/1.22 % (1737107)Time elapsed: 0.068 s
% 3.65/1.22 % (1737107)Peak memory usage: 89 MB
% 3.65/1.22 % (1737107)Instructions burned: 118 (million)
% 3.65/1.22 % (1737115)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1128145335:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.65/1.22 % (1737115)Refutation not found, incomplete strategy
% 3.65/1.22 % (1737115)------------------------------
% 3.65/1.22 % (1737115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.22 % (1737115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.22 % (1737115)CaDiCaL version: 2.1.3
% 3.65/1.22 % (1737115)Termination reason: Refutation not found, incomplete strategy
% 3.65/1.22 % (1737115)Time elapsed: 0.006 s
% 3.65/1.22 % (1737115)Peak memory usage: 88 MB
% 3.65/1.22 % (1737115)Instructions burned: 8 (million)
% 3.65/1.22 % (1737116)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2218671345:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.65/1.22 % (1737117)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2508566112:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.65/1.22 % (1737106)Refutation found. Thanks to Tanya!
% 3.65/1.22 % SZS status Unsatisfiable for theBenchmark
% 3.65/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.22 % (1737106)------------------------------
% 3.65/1.22 % (1737106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.22 % (1737106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.22 % (1737106)CaDiCaL version: 2.1.3
% 3.65/1.22 % (1737106)Termination reason: Refutation
% 3.65/1.22 % (1737106)Time elapsed: 0.035 s
% 3.65/1.22 % (1737106)Peak memory usage: 89 MB
% 3.65/1.22 % (1737106)Instructions burned: 52 (million)
% 3.65/1.22 % (1737106)------------------------------
% 3.65/1.22 % (1737106)------------------------------
% 3.65/1.22 % (1737096)Success in time 0.463 s
% 3.65/1.22 % Vampire exiting
%------------------------------------------------------------------------------